Table of Contents
- 1 BoB ASIRI 2013 CTD χpod
- 2 Read in other datasets
- 3 Using climatological gradients
- 4 Naveira Garabato et al. (2016) approach
- 5 Ferrari & Polzin (2005) approach
- 6 Without interpolating to convert to density space
- 7 Compare various mean fields / gradients
- 8 Argo estimate (Cole et al, 2015)
- 9 All data combined
- 10 Lessons learned
- 11 Groupby on dataframe or xarray consistently
- 12 Test gradients in isopycnal planes
- 13 Convert transect .mat to netcdf files
BoB ASIRI 2013 CTD χpod¶
This notebook will attempt to infer eddy diffusivity $K_e$ from the basin-wide transect of $χ, K_T$
\begin{equation} K_e = \frac{⟨\widetilde{χ}⟩/2 - ⟨K_T \, ∂_z \widetilde{θ}⟩ \; ∂_z θ_m}{|∇θ_m|²} \end{equation}
In [2]:
import sys
sys.path.append('../eddydiff/')
import eddydiff as ed
Transect TS plots¶
In [57]:
tr1 = xr.open_dataset('../datasets/bob-ctd-chipod/transect_1.nc', autoclose=True)
tr2 = xr.open_dataset('../datasets/bob-ctd-chipod/transect_2.nc', autoclose=True)
tr3 = xr.open_dataset('../datasets/bob-ctd-chipod/transect_3.nc', autoclose=True)
_, bins = pd.cut(tr1.rho.values.ravel(), 8, retbins=True)
dcpy.oceans.TSplot(tr1.S, tr1['T'], tr1.pres, rho_levels=bins-1000)
plt.title('Transect 1')
plt.savefig('../images/bob-TS-transect-1.png', bbox_inches='tight')
dcpy.oceans.TSplot(tr2.S, tr2['T'], tr2.pres, rho_levels=bins-1000)
plt.title('Transect 2')
plt.savefig('../images/bob-TS-transect-2.png', bbox_inches='tight')
dcpy.oceans.TSplot(tr3.S, tr3['T'], tr3.pres, rho_levels=bins-1000)
plt.title('Transect 3')
plt.savefig('../images/bob-TS-transect-3.png', bbox_inches='tight')
Read and plot single transect¶
In [339]:
transect = (xr.open_dataset('../datasets/bob-ctd-chipod/transect_1.nc', autoclose=True)
.sel(cast=slice(10, 36)))
transect['KtTz'] = transect['KT'] * transect['dTdz']
transect['Jq'] = 1025 * 4200 * transect['KtTz']
transect['KtTz'].values[np.abs(transect['Jq'].values) > 500] = np.nan
transect['Jq'].values[np.abs(transect['Jq'].values) > 500] = np.nan
np.log10(transect['KT']).plot(robust=True, yincrease=False)
plt.figure()
transect['dTdz'].plot(robust=True, yincrease=False)
plt.figure()
np.log10(transect['KtTz']).plot(robust=True, yincrease=False)
plt.figure()
transect['T'].sel(cast=slice(10, 36)).plot.contour(
levels=40, colors='k', robust=True, yincrease=False)
transect['rho'].sel(cast=slice(10, 36)).plot.contour(
levels=20, colors='r', robust=True, yincrease=False)
plt.title('black=T, red=ρ')
# transect = transect.drop(30, dim='cast').sel(P=slice(None, 110))
Out[339]:
Make sure $J_q$ isn't crazy
In [340]:
np.log10(np.abs(transect['Jq'])).plot.hist()
Out[340]:
Process transect data¶
In [3]:
transect = (xr.open_dataset('../datasets/bob-ctd-chipod/transect_1.nc', autoclose=True)
.sel(cast=slice(10, 36)))
transect['KtTz'] = transect['KT'] * transect['dTdz']
transect['Jq'] = 1025 * 4200 * transect['KtTz']
transect['KtTz'].values[np.abs(transect['Jq'].values) > 1000] = np.nan
transect['Jq'].values[np.abs(transect['Jq'].values) > 1000] = np.nan
transect = transect.sel(P=slice(None, 210))
# def process_transect
# takes transect in z-space as input.
trmean_rho = ed.transect_to_density_space(transect)
Read in other datasets¶
In [8]:
cole = ed.read_cole()
argograd = xr.open_dataset('../datasets/argo_dec_iso_gradients.nc',
decode_times=False, autoclose=True).load()
eccograd = xr.open_dataset('../datasets/ecco_monthly_iso_gradient.nc',
decode_times=False, autoclose=True).load()
Using climatological gradients¶
\begin{equation} K_e = \frac{⟨\widetilde{χ}⟩/2 - ⟨K_T \, ∂_z \widetilde{θ}⟩ \; ∂_z θ_m}{|∇θ_m|²} \end{equation}
In [14]:
eccoKe = ed.process_transect_1d(transect, eccograd, 'ECCO transect1')
argoKe = ed.process_transect_1d(transect, argograd, 'ARGO transect1')
Ke = pd.DataFrame()
Ke['ecco'] = eccoKe.Ke
Ke['argo'] = argoKe.Ke
# Ke['rho'] = Ke.ecco.index.mid.astype('float')
eccoKe
Out[14]:
In [16]:
ed.plot_bar_Ke(eccoKe)
# ed.plot_bar_Ke(argoKe)
In [30]:
plt.figure()
argomean.dTdia.plot(x='rho')
eccomean.dTdia.plot(x='rho')
(trmean.dTdz).plot(x='rho')
plt.legend(['argo', 'ecco', 'transect'])
plt.figure()
argomean.dTiso.plot(x='rho')
eccomean.dTiso.plot(x='rho')
In [12]:
(ecco.dTiso.sel(lat=slice(transect.lat.min(), transect.lat.max()))
.sel(lon=transect.lon.mean(), method='nearest')
.plot.contourf(robust=True, yincrease=False))
(ecco.Tmean.sel(lat=slice(transect.lat.min(), transect.lat.max()))
.sel(lon=transect.lon.mean(), method='nearest')
.plot.contour(robust=True, colors='w', yincrease=False))
plt.gca().set_ylim([200, 0])
Naveira Garabato et al. (2016) approach¶
For turbulence quantities, the averaging operator ⟨⟩ operates only in the vertical direction.
Mean temperature field is determined by spline smoothing on isopycnals and then differentiated to get "large-scale" gradients.
Calculation¶
In [470]:
# 1. convert to density space
#############################
trdens = ed.to_density_space(transect1)
Tdens = trdens['T']
# 2. fit cubic spline along isopycnal
# - this needs to take ρbins as input?
#####################################
Tdens_i = ed.smooth_cubic_spline(trdens['T'], False)
Pdens_i = ed.smooth_cubic_spline(trdens['P'], False)
Tsmooth = ed.to_depth_space(Tdens_i, Pold=Pdens_i, Pnew=None)
# 3. calculate gradients with smoothed field
############################################
dTiso, dTdia = ed.calc_iso_dia_gradients(Tdens_i, Pdens_i)
dTmdz = ed.to_density_space(-ed.xgradient(Tsmooth, 'P'))
dTmdz.name = 'dz'
# 4. Bin smoothed gradients by density
######################################
ρbins = Tdens_i.rho[::2]
dTdf = (ed.exchange(xr.merge([dTdia, dTiso]),
{'cast': 'dist'})
.to_dataframe()
.reset_index())
dTmean = ed.bin_avg_in_density(dTdf, ρbins)
transmean = ed.bin_avg_in_density(trdens.to_dataframe().reset_index(), ρbins)
# 5. do estimate
################
transKe = xr.Dataset()
transKe['Ke'] = (transmean.chi/2 - transmean.KtTz * dTmean.dia)/dTmean.iso**2
transKe.Ke.name = '$K_e$'
transKe['KT'] = transmean.KT
transKe['KtTz'] = transmean.KtTz
transKe['dTdz'] = transmean.dTdz
transKe['chi'] = transmean.chi
transKe['dTmdz'] = dTmean.dia
transKe['dTiso'] = dTmean.iso
transKe['rho'].values = np.round(transKe.rho.values, decimals=2)
transKe.attrs.name = 'BoB CTD χpod'
ed.plot_transect_Ke(transKe)
ed.plot_bar_Ke(transKe.isel(cast=20).to_dataframe())
Debugging plots¶
In [471]:
trdens = ed.to_density_space(transect1)
Tdens = trdens['T']trdens['P'].plot.contour(levels=20)
dcpy.ts.xfilter(trdens['P'], dim='cast', flen=10).plot.contour(
colors='r', levels=20)
Pdens_i.plot.contour(levels=20, colors='k')
Out[471]:
Distributions: dT/dz and dT_diapycnal¶
The distributions of (dT/dz)_ρ is different from (dT/dz)_z which is maybe not surprising but the difference is a factor of 2, this makes me suspicious.
In [73]:
dTi, dTd = ed.calc_iso_dia_gradients(trdens['T'], trdens['P'])
dTi_i, dTd_i = ed.calc_iso_dia_gradients(Tdens_i, Pdens_i)
histargs = {'histtype': 'step'}
f, ax = plt.subplots(1, 2)
dTi.plot.hist(ax=ax[0], **histargs)
dTi_i.plot.hist(ax=ax[0], **histargs)
ax[0].legend(['dTiso of T interp to ρ space',
'dTiso of spline smooth T'])
dTd.plot.hist(ax=ax[1], **histargs)
dTd_i.plot.hist(ax=ax[1], **histargs)
trdens['dTdz'].plot.hist(ax=ax[1], **histargs)
transect['dTdz'].plot.hist(ax=ax[1], **histargs)
dTmdz.plot.hist(ax=ax[1], **histargs)
plt.gca().legend(['dTdia of T interp to ρ space',
'dTdia of spline smooth T',
'local dTdz interp to ρ space',
'observed local dTdz',
'dTdz of spline smooth T after moving to z space'])
f.set_size_inches(9, 5)
In [15]:
%matplotlib inline
plt.scatter(xr.broadcast(trdens['dist'], Pdens_i)[0].T,
Pdens_i, 20, dTd_i, cmap=mpl.cm.RdYlBu)
plt.gca().invert_yaxis()
plt.colorbar()
transect['T'].plot.contour(colors='r', levels=30, yincrease=False)
transect['rho'].plot.contour(levels=25, colors='k', yincrease=False)
Out[15]:
In [20]:
%matplotlib inline
plt.scatter(xr.broadcast(trdens['dist'], Pdens_i)[0].T,
Pdens_i, 20, dTd_i, cmap=mpl.cm.RdYlBu)
plt.gca().invert_yaxis()
plt.colorbar()
Out[20]:
In [326]:
###################################
# sample mean fields along transect
###################################
seltrans = dict(lon=transect.lon, lat=transect.lat, method='nearest')
f, ax = plt.subplots(4, 1)
f.set_size_inches(8, 14)
(eccograd.dTiso.sel(pres=slice(200, 0, -1)).sel(**seltrans)
.plot(ax=ax[0], cmap=mpl.cm.Reds))
(eccograd.Tmean.sel(pres=slice(200, 0, -1)).sel(**seltrans)
.plot.contour(ax=ax[0], levels=20, colors='w'))
ax[0].set_ylim([200, 0])
# plots
Tdens.plot.contourf(levels=50, ax=ax[1], cmap=mpl.cm.RdYlBu_r, yincrease=False)
Tdens_i.plot.contour(levels=50, colors='k', ax=ax[1], yincrease=False)
trdens.P.plot.contour(levels=20, colors='lightgray', ax=ax[1], yincrease=False)
np.abs(dTiso).plot(ax=ax[2], cmap=mpl.cm.Reds, robust=True, yincrease=False)
Tdens_i.plot.contour(levels=50, colors='k', ax=ax[2], yincrease=False)
#trdens.P.plot.contour(levels=20, colors='lightgray', ax=ax[2], yincrease=False)
dTdia.plot(ax=ax[3], robust=True, yincrease=False)
Tdens_i.plot.contour(levels=50, colors='k', ax=ax[3], yincrease=False)
Pdens_i.plot.contour(levels=20, colors='lightgray', ax=ax[3], yincrease=False)
In [18]:
f, ax = plt.subplots(2,1)
f.set_size_inches(8,6)
trdens['P'].plot.contour(ax=ax[0], yincrease=False, levels=50, colors='k')
Pdens_i.plot.contour(ax=ax[0], yincrease=False, levels=40, cmap=mpl.cm.Blues)
transect['rho'].plot.contour(ax=ax[1], yincrease=False, levels=50)
ax[1].set_ylim([100, 0])
Out[18]:
Ferrari & Polzin (2005) approach¶
They average all data on density surfaces, estimate mean depth of isopycnal $z_n$ and calculate diapycnal gradient. The result is a vertical profile of eddy diffusivity. All spatial variations are averaged over.
They calculate an isopycnal gradient by doing a plane fit along isopycnals to all the data. This is required for the finestructure estimate
In [76]:
transKe
Out[76]:
In [323]:
# def transect_fp(trdens):
trdens = ed.to_density_space(transect)
dTiso = xr.DataArray(np.ones_like(trdens.rho) * np.nan,
dims=['rho'], coords={'rho': trdens.rho})
# fit straight lines to get mean gradients
# FP do a plane fit in 2D
for idx, rr in enumerate(trdens.rho):
Tvec = trdens['T'].sel(rho=rr)
mask = ~np.isnan(Tvec)
if mask.sum() < 3:
continue
dTiso[idx], _, _, _, _ = sp.stats.linregress(trdens.dist[mask]*1000, Tvec[mask] )
trmean = trdens.mean(dim='cast')
trmean
Tmean = ed.to_depth_space(trmean['T'].expand_dims(['cast']),
Pold=trmean['P'].expand_dims(['cast'])).mean(dim='cast')
rhomean = ed.to_depth_space(trmean['rho'].expand_dims(['cast']),
Pold=trmean['P'].expand_dims(['cast'])).mean(dim='cast')
_, Tsmooth = ed.fit_spline(Tmean.P, Tmean, k=2)
# Tmean.plot()
dTdz = ed.xgradient(-Tsmooth, dim='P')
dTdz.coords['rho'] = rhomean
dTdz = dTdz.expand_dims(['cast'])
dTdz['rho'] = dTdz.rho.expand_dims(['cast'])
dTmdz = ed.to_density_space(dTdz).mean(dim='cast')
fpKe = xr.Dataset()
fpKe['chi'] = trmean.chi
fpKe['dTmdz'] = trmean.dTdz
fpKe['dTiso'] = dTiso
fpKe['KtTz'] = trmean.KtTz
fpKe['KT'] = trmean.KT
fpKe['dTdz'] = trmean.dTdz
fpKe['Ke'] = np.abs(fpKe.chi/2 - fpKe.KtTz * fpKe.dTmdz)/fpKe.dTiso**2
ed.plot_bar_Ke(fpKe.to_dataframe())
Without interpolating to convert to density space¶
In [472]:
mask= ~np.isnan(trmean_rho['T'].isel(rho=5))
ed.fit_spline(trmean_rho['dist'][mask].values,
trmean_rho['T'].isel(rho=5)[mask].values, debug=True)
Out[472]:
In [449]:
# Run Section 1.3 first
# 2. Generate mean field T, P using cubic splines to smooth
# Calculate Trms as RMS of deviations from smoothed T field
trmean_rho['Tmean'] = ed.smooth_cubic_spline(trmean_rho['T'])
trmean_rho.Tmean.attrs['name'] = 'Smoothed temperature'
trmean_rho['Pmean'] = ed.smooth_cubic_spline(trmean_rho['P'])
trmean_rho.Pmean.attrs['name'] = 'Smoothed pressure'
def check_spline_smoothing(T, Ts, P, Ps, Traw, Praw):
f, ax = plt.subplots(3, 1)
T.plot.contour(ax=ax[0], y='rho', levels=50, colors='r')
Ts.plot.contour(ax=ax[0], y='rho', levels=50, colors='k', yincrease=False)
P.plot.contour(ax=ax[1], y='rho', levels=50, colors='r')
Ps.plot.contour(ax=ax[1], y='rho', levels=50, colors='k', yincrease=False)
#cmat, rhomat = xr.broadcast(T.cast, T.rho)
#ax[2].contour(cmat, P, T, levels=50, colors='r')
Tz = ed.to_depth_space(T, P)
Tzs = ed.to_depth_space(Ts, Ps)
ax[2].contour(xr.broadcast(Traw.cast, Praw)[0], Praw.T, Traw.T, 50,
cmap=mpl.cm.BuGn)
Tz.plot.contour(ax=ax[2], x='cast', levels=30, colors='r')
Tzs.plot.contour(ax=ax[2], x='cast', levels=30,
colors='k', yincrease=False)
f.set_size_inches((8, 10))
ax[0].set_title('Smoothed temp')
ax[1].set_title('Smoothed pressure')
ax[2].set_title('Raw and smoothed temperature in depth space')
ax[2].set_ylim([220, 0])
plt.tight_layout()
check_spline_smoothing(trmean_rho['T'], trmean_rho['Tmean'],
trmean_rho['P'], trmean_rho['Pmean'],
transect['T'], transect['pres'])
trmean_rho['Trms'] = np.sqrt(
((trmean_rho['T'] - trmean_rho['Tmean'])**2).mean(dim='cast'))
trmean_rho.Trms.attrs['name'] = 'RMS temp variations'
In [515]:
# 3. Calculate isopyncal and diapycnal gradients of the mean field
trmean_rho['dTiso'], trmean_rho['dTdia'] = \
ed.calc_iso_dia_gradients(trmean_rho['Tmean'], trmean_rho['Pmean'], debug=True)
trmean_rho.dTiso.attrs['name'] = 'Isopycnal ∇T'
trmean_rho.dTdia.attrs['name'] = 'Diapycnal ∇T'
In [516]:
transKe = xr.Dataset()
transKe['KT'] = trmean_rho.KT
transKe['KtTz'] = trmean_rho.KtTz
transKe['dTdz'] = trmean_rho.dTdz
transKe['chi'] = trmean_rho.chi
transKe['dTmdz'] = trmean_rho.dTdia
transKe['dTiso'] = trmean_rho.dTiso
transKe['rho'].values = np.round(transKe.rho.values, decimals=2)
transKe['Tm'] = trmean_rho['Tmean']
transKe.attrs['name'] = 'BoB CTD χpod'
def calc_Ke(transKe, navg=None):
transKe = transKe.copy()
if navg is not None and np.isinf(navg):
transKe = transKe.mean(dim='cast')
elif navg is not None:
cbins = np.arange(transKe.cast.min(), transKe.cast.max()+1, navg)
transKe = (transKe.groupby_bins('cast', cbins, labels=cbins[:-1]+1)
.mean(dim='cast'))
transKe['Ke'] = (transKe.chi/2 - transKe.KtTz *
transKe.dTmdz)/transKe.dTiso**2
transKe.Ke.values[np.abs(transKe.dTiso.values) < 5e-7] = np.nan
transKe.Ke['name'] = '$K_e$'
transKe.attrs['navg'] = navg
if 'cast_bins' in transKe.coords:
transKe = transKe.rename({'cast_bins': 'cast'})
return transKe
transKe = calc_Ke(transKe)
ed.plot_transect_Ke(transKe)
In [452]:
transKe2 = calc_Ke(transKe, navg=None)
ax, axback = ed.plot_transect_var(x='cast', y='rho', data=transKe2.Ke,
fill=trmean_rho['dTiso'], contour=trmean_rho['P'],
xlim=[1, 1e4], xticks=[1e3])
ax, axback = ed.plot_transect_var(x='cast', y='rho', data=transKe2.chi/2,
bar2=transKe2.KtTz * transKe2.dTmdz,
fill=trmean_rho['T'], contour=trmean_rho['P'])
In [439]:
transKe2.Ke.plot.line(y='rho', hue='cast', yincrease=False)
plt.gca().set_xscale('log')
plt.gca().set_xlim([1e2, 1e5])
cole = ed.read_cole()
region = ed.get_region_from_transect(transect)
cole_bay = (cole.sel(lat=region['lat'])).mean(dim='lon').mean(dim='lat')
cole_bay['density_mean_depth'] += 1000
cole_bay = cole_bay.set_coords('density_mean_depth')
cole_bay.diffusivity.plot(y='density_mean_depth', color='k', yincrease=False)
Out[439]:
In [517]:
transKe2.Ke.where(transKe2.Ke > 0).mean(dim='cast').plot.line(y='rho')
cole_bay = (cole.sel(lat=region['lat'])).mean(dim='lon').mean(dim='lat')
cole_bay['density_mean_depth'] += 1000
cole_bay = cole_bay.set_coords('density_mean_depth')
cole_bay.diffusivity.plot(y='density_mean_depth', color='k', yincrease=False)
plt.gca().set_xscale('log')
plt.gca().set_xlim([1e2, 1e5])
plt.figlegend(['Mean in along-transect direction', 'Cole et al (2015)'])
Out[517]:
Compare various mean fields / gradients¶
In [34]:
argo = xr.open_dataset('../datasets/argo_clim_iso_gradients.nc',
decode_times=False, autoclose=True).load()
ecco = xr.open_dataset('../datasets/ecco_annual_iso_gradient.nc',
autoclose=True).load()
In [44]:
region = ed.get_region_from_transect(transect)
argo.dTiso.sel(**region).mean(dim='lon').plot(robust=True, yincrease=False)
plt.figure()
ecco.dTiso.sel(**region).mean(dim='lon').plot(robust=True, yincrease=False)
plt.figure()
np.abs(trmean_rho.dTiso).plot(robust=True, yincrease=False)
Out[44]:
Argo estimate (Cole et al, 2015)¶
In [459]:
region = ed.get_region_from_transect(transect)
cole_bay = (cole.sel(lat=region['lat'], lon=region['lon']))
(cole_bay.diffusivity.mean(dim='lon')
.plot(y='depth', yincrease=False,
norm=mpl.colors.LogNorm(),
cmap=mpl.cm.Reds))
plt.gca().set_ylim([200, 0])
Out[459]:
In [513]:
(cole_bay.diffusivity.mean(dim='lat').mean(dim='lon')
.plot.line(y='depth', yincrease=False))
plt.gca().set_xscale('log')
plt.gca().set_xlim([1e2, 3e4])
plt.gca().set_ylim([200, 0])
plt.gca().grid(True)
In [514]:
(cole_bay.diffusivity.groupby_bins(cole_bay.density_mean_depth+1000,
ρbins,
labels=(ρbins[:-1]+ρbins[1:])/2).mean()
.plot.line(y='density_mean_depth_bins', yincrease=False))
Out[514]:
All data combined¶
Let's ignore 3 for now, not sure why that overlaps.
In [6]:
transect1 = (xr.open_dataset('../datasets/bob-ctd-chipod/transect_1.nc', autoclose=True))
transect2 = (xr.open_dataset('../datasets/bob-ctd-chipod/transect_2.nc', autoclose=True))
transect3 = (xr.open_dataset('../datasets/bob-ctd-chipod/transect_3.nc', autoclose=True))
plt.plot(transect1.lon, transect1.lat, '.', ms=20)
plt.plot(transect2.lon, transect2.lat, '.', ms=20)
plt.plot(transect3.lon, transect3.lat, 'o')
plt.legend(('big(1)', 'big(2)', 'big(3)'))
Out[6]:
In [9]:
# merge transect 1 and transect2
transect = pd.concat([tr.to_dataframe().reset_index()
for tr in [transect1.sel(P=slice(0, 120))]])
transect['KtTz'] = transect['KT'] * transect['dTdz']
transect['Jq'] = 1025 * 4200 * transect['KtTz']
mask = np.logical_or(np.abs(transect['Jq'].values) > 2000,
transect['KT'].values > 5e-3)
transect['KtTz'].values[mask] = np.nan
transect['Jq'].values[mask] = np.nan
transect['chi'].values[mask] = np.nan
eccoKe2 = ed.process_transect_1d(transect, eccograd, 'ECCO')
argoKe2 = ed.process_transect_1d(transect, argograd, 'ARGO')
ed.plot_bar_Ke(eccoKe2)
ed.plot_bar_Ke(argoKe2)
eccoKe2.Ke
Out[9]:
In [467]:
transect1['T'].sel(cast=slice(9, 40)).plot(cmap=mpl.cm.RdYlBu_r, yincrease=False)
transect1['rho'].sel(cast=slice(9, 40)).plot.contour(colors='k',
levels=np.arange(1020, 1028),
yincrease=False)
plt.figure()
(eccograd['ρmean'].sel(**ed.get_region_from_transect(transect1))
.mean(dim='lon')
.plot.contour(levels=np.arange(1020, 1028), colors='k', yincrease=False))
plt.gca().set_ylim([200, 0])
Out[467]:
In [468]:
trmean, ρbins = ed.average_transect_1d(transect)
eccomean = ed.average_clim(eccograd, transect, ρbins)
eccomean
Out[468]:
In [22]:
sp, Tsm = ed.fit_spline(eccomean['Pmean'], eccomean['Tmean'], k=3, debug=False)
plt.plot(sp.derivative(1)(eccomean['Pmean']))
plt.plot(-eccomean.dTdz.values)
Lessons learned¶
Don't interpolate when converting to density space¶
+The fields and gradients are different!+
FALSE ALARM: This is because transect.P and transect.pres are different!
In [39]:
# transform to depth space, calculate gradient and transform back
Tsmooth = ed.to_depth_space(Tdens_i, Pold=Pdens_i, Pnew=None)
dTmdz = (-ed.xgradient(Tsmooth, 'P'))
ed.to_density_space(dTmdz).plot(yincrease=False)
# original calculation ΔT and ΔP are estimated in density space
plt.figure()
trmean_rho.dTdia.plot(yincrease=False, x='cast')
Out[39]:
Spline-smooth both temperature and pressure¶
Below I calculate dT/dP in density space and compare that to dT/dP calculated by
- transforming spline smoothed T to pressure space
- differentiate to get dT/dP
- convert back to density space and plot.
In [38]:
trdens = ed.to_density_space(transect)
plt.close('all')
Tdens_i = ed.smooth_cubic_spline(trdens['T'], False)
Pdens_i = ed.smooth_cubic_spline(trdens['P'], False)
levels = np.linspace(trdens['T'].min(), trdens['T'].max(), 40)
trdens['T'].plot.contour(colors='r', levels=levels)
Tdens_i.plot.contour(colors='k', levels=levels, yincrease=False)
plt.title('In ρ space')
plt.figure()
Tsmooth = ed.to_depth_space(Tdens_i, Pold=Pdens_i, Pnew=None)
transect['T'].plot.contour(colors='r', levels=levels, yincrease=False)
Tsmooth.plot.contour(colors='k', levels=levels, yincrease=False)
plt.title('To depth space using spline smoothed pressure')
plt.ylim([120, 0])
plt.figure()
psmooth = dcpy.ts.xfilter(trdens['P'], dim='cast', flen=10)
Tsmooth = ed.to_depth_space(Tdens_i, Pold=psmooth, Pnew=None)
transect['T'].plot.contour(colors='r', levels=levels, yincrease=False)
Tsmooth.plot.contour(colors='k', levels=levels, yincrease=False)
plt.title('To depth space using hann smoothed pressure')
plt.ylim([120, 0])
plt.figure()
Tsmooth = ed.to_depth_space(Tdens_i, Pold=trdens['P'], Pnew=None)
transect['T'].plot.contour(colors='r', levels=levels, yincrease=False)
Tsmooth.plot.contour(colors='k', levels=levels, yincrease=False)
plt.title('To depth space using unsmoothed pressure')
plt.ylim([120, 0])
Out[38]:
Groupby on dataframe or xarray consistently¶
xarray seems to use a different kind of index with groupby_bins.
Test gradients in isopycnal planes¶
In [25]:
coords = {'cast': np.linspace(1, 50, 50),
'P': np.linspace(0, 500, 200)}
T = xr.DataArray(np.ones((len(coords['P']), len(coords['cast']))) * np.nan,
dims=['P', 'cast'], coords=coords, name='T')
T = - 0.6 * T.P + 0.05 * T.cast
T.name = 'T'
rho = 1025 * (1 - 1.7e-4 * (T-15))
rho.name = '$ρ$'
T.plot.contourf(levels=20)
rho.plot.contour(colors='k', yincrease=False)
dT = ed.gradient(T.rename({'P': 'z', 'cast': 'x'}))
dT['dy'] = xr.zeros_like(dT['dx'])
dT.attrs['name'] = 'dT'
drho = ed.gradient(rho.rename({'P': 'z', 'cast': 'x'}))
drho['dy'] = xr.zeros_like(drho['dx'])
drho.attrs['name'] = 'dρ'
dT
Out[25]:
Convert transect .mat to netcdf files¶
In [5]:
ed.convert_mat_to_netcdf()